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Periodic solutions of Hamiltonian systems of 3-body type. (English) Zbl 0745.34034
The existence of \(T\)-periodic solutions of Hamiltonian systems of the form \(\ddot q+V_ q(t,v)=0\) is studied, where \(V=\sum^ 3_{1\leq i\neq j}V_{ij}(t,q_ i-q_ 2)\) is of 3-body type, \(V(t,\xi)\) is \(T\)- periodic in \(t\) and singular at \(\xi=0\). Under these hypotheses, provided that the singularity of \(V\) at 0 is strong enough, it is proved that the functional \(\int^ T_ 0\left({1\over 2}|\dot q|^ 2- V(t,q)\right)dt\) has an unbounded sequence of critical points, which correspond to the \(T\)-periodic solutions of the considered equation.
Reviewer: I.Ginchev (Varna)

MSC:
34C25 Periodic solutions to ordinary differential equations
37J99 Dynamical aspects of finite-dimensional Hamiltonian and Lagrangian systems
70F07 Three-body problems
58E05 Abstract critical point theory (Morse theory, Lyusternik-Shnirel’man theory, etc.) in infinite-dimensional spaces
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